System Comparison

In the initial set of experiments, we compare the successful packet transmission of our hybrid system to the centralized system developed by Fink et al. There were three sets of experiments run for this section. Each set consisted of ten trials, with only one data flow, a1

4,m = 0.5. The

first two sets provide the comparison between the hybrid and centralized systems in Levine-GRW, while the third highlights the performance of the hybrid system in a different environment, the Towne building. For the first two sets, the centralized planner was used to find the trajectories that allowed the team to complete the goal, which was reach the blue square from the initial formation shown in Fig. 4.2a. With these trajectories the waypoint generator was used to reduce the number of waypoints to three as shown in Fig. 4.5. These sets of waypoints were then used by both the centralized motion controller and the local controllers, to remove any bias incurred by different input waypoints. The results of the ten trials are plotted in Fig. 4.6a, where the solid line represents the average over all the trials and the dotted envelope shows the oneσbounds. There are a few items to note; first, there is a portion of the data in which the average success rate for the centralized system falls below 0.5; this is mostly due to a mismatch between the channel model

Distance (m) 4 6 8 10 12 14 16 18 20 Success Rate 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Levine-GRW Hybrid Centralized

(a) Experimental results for centralized and hy- brid systems in Levine-GRW. The solid line is the average performance and the dashed colored

lines are +/- 1 σ bounds. The black dashed

line is the minimum input data rate for the lead robot. Distance (m) 4 6 8 10 12 14 16 18 20 22 Success Rate 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Towne Hybrid

(b) Experimental results for the hybrid system

in the Towne building. The solid line is the

average performance and the dashed line is the

+/- 1 σ bounds. The red dashed line is the

minimum input data rate for the lead robot.

Figure 4.6: Experimental results for Levine-GRW and the Towne building.

and the actual environment. The second item to notice is how well the hybrid system performs. Even the oneσbound stays above the required data rate. This is mostly due to the robots locally optimizing their trajectory and not moving in straight lines. Another item to note is the spread on the oneσbounds. Since the centralized system is including an estimate of the channel variance the spread is much less than the hybrid system which is only a proxy for the channel variance. Also, since the hybrid system allows for deviations to locally optimize, the trajectories taken by the robots is not always the same compared to the tightly controlled trajectories executed by the centralized system. The final item to note is the divergence of the results for the two systems at 12 meters. While the hybrid system continues to exceed the required data rates, the centralized system drops off dramatically to marginally meeting the requirements. The reason for this is at 12 meters the sensing robot turns the corner and must rely on the support robots to relay data back to the access point. Since the centralized system is planning for future unknown links rates it adopts a conservative approach with respect to a single link. This conservative approach is useful when planning but it does not leverage the current state of the environment and team formation.

In contrast the local controller in the hybrid system is constantly optimizing for performance based on the environment and team’s formation. Therefore, it can achieve a higher level of performance when compared to the centralized systems due to better utilization of current information. An example of this is seen in Fig. 4.7, where the location and routing probabilities are plotted for one trial of the experiment. For both systems, two snapshots in time are taken, t = 120 and at the completion of the task. In the first time instance, the formations are not identical. This is due to the local deviations performed by the hybrid system, but the final formations match.

In the third set of experiments for this section the same task, drive around a corner, was completed but in the Towne building shown in Fig. 4.2c. Again, the hybrid system was given the blue square as a goal location for the sensing robot, and the initial formation is indicated by the red circles. Ten experiments were run with a1

1,m = 0.5, and the results are plotted in Fig. 4.6b.

The system performs remarkably well, with the one σ bounds well above the desired results. This is most likely due to the Towne building having wider hallways compared to Levine-GRW and therefore the amount of multi-path interference being reduced when the robots are in the center of the hallway. Also, the same model parameters were used as in Levine-GRW; thus the superior performance could indicate that the channel model is conservative with respect to the RF environment in Towne when compared to Levine-GRW.